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...y consider power series in a complex variable <math>z-a</math> for a fixed complex number ''a''.

{{r|Complex number}}

Any complex number <math>z=(a,b)</math> can be written as <math>z=a+bi</math> (this is often c {{Image|Complex_plane3.png|right|250px|Fig. 1. Graphical representation of a complex number and its conjugate}}

...specifically&mdash;in [[number theory]], an '''algebraic number''' is a [[complex number]] that is a root of a [[polynomial]] with [[rational number|rational]] coef ...s. It follows that the term "algebraic number" can also be defined as a [[complex number]] that is a root of a [[polynomial]] with [[integer]] coefficients. If an

...the Hermitian conjugate of a complex [[matrix]] to linear operators on [[complex number|complex]] [[Hilbert space|Hilbert spaces]]. In this article the adjoint of The fact that the complex conjugate of the complex number ''a'' appears is due to the property of the inner product on complex Hilber

{{r|Complex number}}

{{r|Complex number}}

...whose coefficients are [[Complex number|complex numbers]] has at least one complex number as a root. In other words, given any polynomial (where <math>d</math> is any positive integer), we can find a complex number <math>t</math> so that

Let ''V'' be a [[complex number|complex]] [[inner product space]] with inner product <math>\langle \cdot,\c ...of vectors in ''V'' and let <math>\phi(x,y)</math> be the argument of the complex number <math>\langle x,y\rangle</math>. Now, consider the expression <math>f(t)=\l

...gebraic numbers can be complex" to the statement "an algebraic number is a complex number...", with the rationale that the second was correct and stronger. ...his embedding. Thus, an algebraic number can generally be thought of as a complex number, but not in a canonical way, and in general it is just an element of some a

{{r|Complex number}}

...dition between the [[Real part|real]] and [[imaginary part]] of a given [[Complex number|complex valued]] function of <var>2n</var> [[real number|real]] [[variable] ..., <var>y</var>) + <var>i</var><var>v</var>(<var>x</var>, <var>y</var>) a [[Complex number|complex valued]] [[differentiable function]]. Then <var>f</var> satisfies t

{{r|Complex number}}

We may embed ''K'' into the [[algebraically closed field]] of [[complex number]]s '''C'''. There are exactly ''n'' such embeddings: we can see this by ta

...r by [[William Rowan Hamilton]] in 1837; this construction is explained [[Complex number#Formal definition|later in this article]].

and in general <math>\lambda</math> can be [[complex number|complex]].

...ssed in terms of the [[Eisenstein integer]]s, that is, the ring ''E'' of [[complex number]]s of the form

{{r|Complex number}}

We see that even when a, b, and c are real numbers, the solutions may be [[complex number]]s."

...iagram. An integer is a Real. A Real(float) is a (subset of) complex. An a complex number is a (subset of) complex matrices, if we think of a (1 by 1) matrix as a si